public void different_sizes_are_not_equal()
{
var a = new VectorF(2);
a.Set(0, 9.0f);
a.Set(1, -10.3f);
var b = new VectorF(3);
b.Set(0, 9.0f);
b.Set(1, -10.3f);
Assert.False(a.Equals(b));
Assert.False(b.Equals(a));
}
public void different_ref_same_components_are_equal()
{
var a = new VectorF(2);
a.Set(0, 9.0f);
a.Set(1, -10.3f);
var b = new VectorF(2);
b.Set(0, 9.0f);
b.Set(1, -10.3f);
Assert.True(a.Equals((object)b));
Assert.True(b.Equals((object)a));
}
public void different_components_are_not_equal()
{
var a = new VectorF(2);
a.Set(0, 9.0f);
a.Set(1, -10.3f);
var b = new VectorF(2);
b.Set(0, -9.0f);
b.Set(1, 20.4f);
Assert.False(a.Equals((object)b));
Assert.False(b.Equals((object)a));
}
public void example_1()
{
var left = new VectorF(5);
left.Set(0, 1);
var right = new VectorF(5);
right.Set(0, 1);
right.Set(2, 1);
var expected = (float)(Math.Acos(1.0 / Math.Sqrt(2.0)));
var actual = left.GetAngleBetween(right);
Assert.Equal(expected, actual, 5);
}
public void can_get_quotient_vector()
{
var source = new VectorF(2);
source.Set(0, 4.5f);
source.Set(1, 888f);
var expected = new VectorF(2);
expected.Set(0, 4.5f / 4.0f);
expected.Set(1, 888f / 4.0f);
var actual = source.GetQuotient(4);
Assert.Equal(expected, actual);
}
public void can_negate()
{
var actual = new VectorF(2);
actual.Set(0, -8.8f);
actual.Set(1, 6.1f);
var expected = new VectorF(2);
expected.Set(0, 8.8f);
expected.Set(1, -6.1f);
actual.Negate();
Assert.Equal(expected, actual);
}
public void can_divide_vector()
{
var actual = new VectorF(2);
actual.Set(0, 4.5f);
actual.Set(1, 888f);
var expected = new VectorF(2);
expected.Set(0, 4.5f / 4.0f);
expected.Set(1, 888f / 4.0f);
actual.Divide(4);
Assert.Equal(expected, actual);
}
public void can_get_negative_vector()
{
var source = new VectorF(2);
source.Set(0, 1.5f);
source.Set(1, -6f);
var expected = new VectorF(2);
expected.Set(0, -1.5f);
expected.Set(1, 6f);
var actual = source.GetNegative();
Assert.Equal(expected, actual);
}
public void copy_constructor_copies_all_componenets()
{
var expected = new VectorF(5);
expected.Set(0, 0);
expected.Set(1, 1);
expected.Set(2, 2);
expected.Set(3, 3);
expected.Set(4, 4);
var actual = new VectorF(expected);
Assert.NotSame(expected, actual);
Assert.Equal(expected, actual);
}
public void array_constructor_assigns_componenets_and_length()
{
var components = new float[] { 4, 5, 6, 7 };
var expected = new VectorF(4);
expected.Set(0, 4);
expected.Set(1, 5);
expected.Set(2, 6);
expected.Set(3, 7);
var actual = new VectorF(components);
Assert.Equal(components.Length, actual.Dimensions);
Assert.Equal(expected, actual);
}
public void right_angle_is_half_pi()
{
var left = new VectorF(4);
left.Set(0, 1);
left.Set(2, 1);
var right = new VectorF(4);
right.Set(1, 1);
right.Set(3, 1);
var expected = (float)(Math.PI / 2.0);
var actual = left.GetAngleBetween(right);
Assert.Equal(expected, actual, 5);
}
public void get_all_element_for_dim_5()
{
var v = new VectorF(5);
v.Set(0, -1.0f);
v.Set(1, 5.7f);
v.Set(2, -0.4f);
v.Set(3, 9.0f);
v.Set(4, -101.1f);
Assert.Equal(-1.0f, v.Get(0));
Assert.Equal(5.7f, v.Get(1));
Assert.Equal(-0.4f, v.Get(2));
Assert.Equal(9.0f, v.Get(3));
Assert.Equal(-101.1f, v.Get(4));
}
/// <summary>
/// Creates the eigenvalue decomposition of the given matrix.
/// </summary>
/// <param name="matrixA">The square matrix A.</param>
/// <exception cref="ArgumentNullException">
/// <paramref name="matrixA"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="matrixA"/> is non-square (rectangular).
/// </exception>
public EigenvalueDecompositionF(MatrixF matrixA)
{
if (matrixA == null)
{
throw new ArgumentNullException("matrixA");
}
if (matrixA.IsSquare == false)
{
throw new ArgumentException("The matrix A must be square.", "matrixA");
}
_n = matrixA.NumberOfColumns;
_d = new VectorF(_n);
_e = new VectorF(_n);
_isSymmetric = matrixA.IsSymmetric;
if (_isSymmetric)
{
_v = matrixA.Clone();
// Tridiagonalize.
ReduceToTridiagonal();
// Diagonalize.
TridiagonalToQL();
}
else
{
_v = new MatrixF(_n, _n);
// Abort if A contains NaN values.
// If we continue with NaN values, we run into an infinite loop.
for (int i = 0; i < _n; i++)
{
for (int j = 0; j < _n; j++)
{
if (Numeric.IsNaN(matrixA[i, j]))
{
_e.Set(float.NaN);
_v.Set(float.NaN);
_d.Set(float.NaN);
return;
}
}
}
// Storage of nonsymmetric Hessenberg form.
MatrixF matrixH = matrixA.Clone();
// Working storage for nonsymmetric algorithm.
float[] ort = new float[_n];
// Reduce to Hessenberg form.
ReduceToHessenberg(matrixH, ort);
// Reduce Hessenberg to real Schur form.
HessenbergToRealSchur(matrixH);
}
}
public void can_get_scaled_vector()
{
var source = new VectorF(3);
source.Set(0, 1);
source.Set(1, 2);
source.Set(2, -4);
var expected = new VectorF(3);
expected.Set(0, 3);
expected.Set(1, 6);
expected.Set(2, -12);
var actual = source.GetScaled(3);
Assert.Equal(expected, actual);
}
public void can_get_scaled_vector()
{
var actual = new VectorF(3);
actual.Set(0, 1);
actual.Set(1, 2);
actual.Set(2, -4);
var expected = new VectorF(3);
expected.Set(0, 3);
expected.Set(1, 6);
expected.Set(2, -12);
actual.Scale(3);
Assert.Equal(expected, actual);
}
public void array_constructor_copies_all_componenets()
{
var arrayValues = new[] { 1.0f, 2.0f, 3.0f };
var expected = new VectorF(3);
expected.Set(0, 1.0f);
expected.Set(1, 2.0f);
expected.Set(2, 3.0f);
var actual = new VectorF(arrayValues);
arrayValues[0] = -99.0f;
arrayValues[1] = -99.0f;
arrayValues[2] = -99.0f;
Assert.Equal(expected, actual);
}
public void can_find_distance_in_both_directions()
{
var a = new VectorF(5);
a.Set(0, 1);
a.Set(1, 2);
a.Set(2, 3);
var b = new VectorF(5);
b.Set(1, -9);
b.Set(2, 5);
b.Set(4, 3);
var expected = a.GetDistanceSquared(b);
var actual = b.GetDistanceSquared(a);
Assert.Equal(expected, actual);
}
public void subtracting_vectors_leaves_right_unchanged()
{
var left = new VectorF(3);
left.Set(0, 1);
left.Set(1, 10);
left.Set(2, 6);
var right = new VectorF(3);
right.Set(0, 10);
right.Set(1, 3);
right.Set(2, 1);
var expectedRight = new VectorF(right);
left.Subtract(right);
Assert.Equal(expectedRight, right);
}
public void can_get_dot()
{
var left = new VectorF(3);
left.Set(0, 1.2f);
left.Set(1, 3.0f);
left.Set(2, -9.0f);
var right = new VectorF(3);
right.Set(0, -1.1f);
right.Set(1, 6.7f);
right.Set(2, 3.3f);
var expected = (left[0] * right[0]) + (left[1] * right[1]) + (left[2] * right[2]);
var actual = left.GetDot(right);
Assert.Equal(expected, actual, 5);
}
public void can_find_distance()
{
var a = new VectorF(5);
a.Set(0, 1);
a.Set(1, 2);
a.Set(2, 3);
var b = new VectorF(5);
b.Set(1, -9);
b.Set(2, 5);
b.Set(3, 2);
b.Set(4, 3);
var expected = 139.0;
var actual = a.GetDistanceSquared(b);
Assert.Equal(expected, actual);
}
public void can_create_axis_unit_vector(int size, int dimension)
{
var expected = new VectorF(size);
expected.Set(dimension, 1.0f);
var actual = VectorF.CreateUnit(size, dimension);
Assert.Equal(expected, actual);
}
protected VectorF CreateIncremenetal(int dimension)
{
var vector = new VectorF(dimension);
for (int i = 0; i < dimension; i++)
{
vector.Set(i, i + 1);
}
return(vector);
}
public void adding_vectors_does_not_mutate_operands()
{
var left = new VectorF(3);
left.Set(0, 1);
left.Set(1, 3);
left.Set(2, -4);
var expectedLeft = new VectorF(left);
var right = new VectorF(3);
right.Set(0, -10);
right.Set(1, 4);
right.Set(2, -20);
var expectedRight = new VectorF(right);
left.GetSum(right);
Assert.Equal(expectedRight, right);
Assert.Equal(expectedLeft, left);
}
public void subtracting_vectors_leaves_operands_unchanged()
{
var left = new VectorF(3);
left.Set(0, 1);
left.Set(1, 10);
left.Set(2, 6);
var expectedLeft = new VectorF(left);
var right = new VectorF(3);
right.Set(0, 10);
right.Set(1, 3);
right.Set(2, 1);
var expectedRight = new VectorF(right);
var result = left.GetDiffernce(right);
Assert.Equal(expectedLeft, left);
Assert.Equal(expectedRight, right);
}
public void can_add_vectors_of_same_size()
{
var actual = new VectorF(3);
actual.Set(0, 1);
actual.Set(1, 3);
actual.Set(2, -4);
var right = new VectorF(3);
right.Set(0, -10);
right.Set(1, 4);
right.Set(2, -20);
var expected = new VectorF(3);
expected.Set(0, -9);
expected.Set(1, 7);
expected.Set(2, -24);
actual.Add(right);
Assert.Equal(expected, actual);
}
public void subtracting_vector_produces_diff_vector()
{
var left = new VectorF(3);
left.Set(0, 1);
left.Set(1, 10);
left.Set(2, 6);
var right = new VectorF(3);
right.Set(0, 10);
right.Set(1, 3);
right.Set(2, 1);
var expected = new VectorF(3);
expected.Set(0, -9);
expected.Set(1, 7);
expected.Set(2, 5);
var actual = left.GetDiffernce(right);
Assert.Equal(expected, actual);
}
public void subtracting_vector_subtracts_from_components()
{
var actual = new VectorF(3);
actual.Set(0, 1);
actual.Set(1, 10);
actual.Set(2, 6);
var right = new VectorF(3);
right.Set(0, 10);
right.Set(1, 3);
right.Set(2, 1);
var expected = new VectorF(3);
expected.Set(0, -9);
expected.Set(1, 7);
expected.Set(2, 5);
actual.Subtract(right);
Assert.Equal(expected, actual);
}
public void Set()
{
VectorF v = new VectorF(5);
v.Set(0.123f);
Assert.AreEqual(5, v.NumberOfElements);
for (int i = 0; i < 5; i++)
Assert.AreEqual(0.123f, v[i]);
v.Set(new VectorF(new float[] { 1, 2, 3, 4, 5 }));
Assert.AreEqual(5, v.NumberOfElements);
Assert.AreEqual(1, v[0]);
Assert.AreEqual(2, v[1]);
Assert.AreEqual(3, v[2]);
Assert.AreEqual(4, v[3]);
Assert.AreEqual(5, v[4]);
v.Set(new float[] { 1, 2, 3, 4, 5 });
Assert.AreEqual(5, v.NumberOfElements);
Assert.AreEqual(1, v[0]);
Assert.AreEqual(2, v[1]);
Assert.AreEqual(3, v[2]);
Assert.AreEqual(4, v[3]);
Assert.AreEqual(5, v[4]);
v.Set(new List<float>(new float[] { 1, 2, 3, 4, 5 }));
Assert.AreEqual(5, v.NumberOfElements);
Assert.AreEqual(1, v[0]);
Assert.AreEqual(2, v[1]);
Assert.AreEqual(3, v[2]);
Assert.AreEqual(4, v[3]);
Assert.AreEqual(5, v[4]);
}
public void ProjectTo2()
{
VectorF unitX = new VectorF(new float[] { 1, 0, 0, 0 });
VectorF unitY = new VectorF(new float[] { 0, 1, 0, 0 });
VectorF unitZ = new VectorF(new float[] { 0, 0, 1, 0 });
VectorF one = new VectorF(new float[] { 1, 1, 1, 1 });
// Project (1, 1, 1) to axes
VectorF projection = new VectorF(new float[] { 1, 1, 1, 0 });
projection.ProjectTo(unitX);
Assert.AreEqual(unitX, projection);
projection.Set(one);
projection.ProjectTo(unitY);
Assert.AreEqual(unitY, projection);
projection.Set(one);
projection.ProjectTo(unitZ);
Assert.AreEqual(unitZ, projection);
// Project axes to (1, 1, 1)
VectorF expected = new VectorF(new float[] { 1, 1, 1, 0 }) / 3.0f;
projection.Set(unitX);
projection.ProjectTo(new VectorF(new float[] { 1, 1, 1, 0 }));
Assert.AreEqual(expected, projection);
projection.Set(unitY);
projection.ProjectTo(new VectorF(new float[] { 1, 1, 1, 0 }));
Assert.AreEqual(expected, projection);
projection.Set(unitZ);
projection.ProjectTo(new VectorF(new float[] { 1, 1, 1, 0 }));
Assert.AreEqual(expected, projection);
}
public SingularValueDecompositionF(MatrixF matrixA)
{
if (matrixA == null)
throw new ArgumentNullException("matrixA");
// Derived from LINPACK code.
// Initialize.
_m = matrixA.NumberOfRows;
_n = matrixA.NumberOfColumns;
MatrixF matrixAClone = matrixA.Clone();
if (_m < _n)
throw new ArgumentException("The number of rows must be greater than or equal to the number of columns.", "matrixA");
int nu = Math.Min(_m, _n);
_s = new VectorF(Math.Min(_m + 1, _n));
_u = new MatrixF(_m, nu); //Jama getU() returns new Matrix(U,_m,Math.min(_m+1,_n)) ?!
_v = new MatrixF(_n, _n);
float[] e = new float[_n];
float[] work = new float[_m];
// Abort if A contains NaN values.
// If we continue with NaN values, we run into an infinite loop.
for (int i = 0; i < _m; i++)
{
for (int j = 0; j < _n; j++)
{
if (Numeric.IsNaN(matrixA[i, j]))
{
_u.Set(float.NaN);
_v.Set(float.NaN);
_s.Set(float.NaN);
return;
}
}
}
// By default, we calculate U and V. To calculate only U or V we can set one of the following
// two constants to false. (This optimization is not yet tested.)
const bool wantu = true;
const bool wantv = true;
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
int nct = Math.Min(_m - 1, _n);
int nrt = Math.Max(0, Math.Min(_n - 2, _m));
for (int k = 0; k < Math.Max(nct, nrt); k++)
{
if (k < nct)
{
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[k].
// Compute 2-norm of k-th column without under/overflow.
_s[k] = 0;
for (int i = k; i < _m; i++)
_s[k] = MathHelper.Hypotenuse(_s[k], matrixAClone[i, k]);
if (_s[k] != 0)
{
if (matrixAClone[k, k] < 0)
_s[k] = -_s[k];
for (int i = k; i < _m; i++)
matrixAClone[i, k] /= _s[k];
matrixAClone[k, k] += 1;
}
_s[k] = -_s[k];
}
for (int j = k + 1; j < _n; j++)
{
if ((k < nct) && (_s[k] != 0))
{
// Apply the transformation.
float t = 0;
for (int i = k; i < _m; i++)
t += matrixAClone[i, k] * matrixAClone[i, j];
t = -t / matrixAClone[k, k];
for (int i = k; i < _m; i++)
matrixAClone[i, j] += t * matrixAClone[i, k];
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
e[j] = matrixAClone[k, j];
}
if (wantu & (k < nct))
{
// Place the transformation in U for subsequent back
// multiplication.
for (int i = k; i < _m; i++)
_u[i, k] = matrixAClone[i, k];
}
if (k < nrt)
{
// Compute the k-th row transformation and place the
// k-th super-diagonal in e[k].
// Compute 2-norm without under/overflow.
e[k] = 0;
for (int i = k + 1; i < _n; i++)
e[k] = MathHelper.Hypotenuse(e[k], e[i]);
if (e[k] != 0)
{
if (e[k + 1] < 0)
e[k] = -e[k];
for (int i = k + 1; i < _n; i++)
e[i] /= e[k];
e[k + 1] += 1;
}
e[k] = -e[k];
if ((k + 1 < _m) && (e[k] != 0))
{
// Apply the transformation.
for (int i = k + 1; i < _m; i++)
work[i] = 0;
for (int j = k + 1; j < _n; j++)
for (int i = k + 1; i < _m; i++)
work[i] += e[j] * matrixAClone[i, j];
for (int j = k + 1; j < _n; j++)
{
float t = -e[j] / e[k + 1];
for (int i = k + 1; i < _m; i++)
matrixAClone[i, j] += t * work[i];
}
}
if (wantv)
{
// Place the transformation in V for subsequent
// back multiplication.
for (int i = k + 1; i < _n; i++)
_v[i, k] = e[i];
}
}
}
// Set up the final bidiagonal matrix or order p.
int p = Math.Min(_n, _m + 1);
if (nct < _n)
_s[nct] = matrixAClone[nct, nct];
if (_m < p)
_s[p - 1] = 0;
if (nrt + 1 < p)
e[nrt] = matrixAClone[nrt, p - 1];
e[p - 1] = 0;
// If required, generate U.
if (wantu)
{
for (int j = nct; j < nu; j++)
{
for (int i = 0; i < _m; i++)
_u[i, j] = 0;
_u[j, j] = 1;
}
for (int k = nct - 1; k >= 0; k--)
{
if (_s[k] != 0)
{
for (int j = k + 1; j < nu; j++)
{
float t = 0;
for (int i = k; i < _m; i++)
t += _u[i, k] * _u[i, j];
t = -t / _u[k, k];
for (int i = k; i < _m; i++)
_u[i, j] += t * _u[i, k];
}
for (int i = k; i < _m; i++)
_u[i, k] = -_u[i, k];
_u[k, k] = 1 + _u[k, k];
for (int i = 0; i < k - 1; i++)
_u[i, k] = 0;
}
else
{
for (int i = 0; i < _m; i++)
_u[i, k] = 0;
_u[k, k] = 1;
}
}
}
// If required, generate V.
if (wantv)
{
for (int k = _n - 1; k >= 0; k--)
{
if ((k < nrt) & (e[k] != 0.0))
{
for (int j = k + 1; j < nu; j++)
{
float t = 0;
for (int i = k + 1; i < _n; i++)
t += _v[i, k] * _v[i, j];
t = -t / _v[k + 1, k];
for (int i = k + 1; i < _n; i++)
_v[i, j] += t * _v[i, k];
}
}
for (int i = 0; i < _n; i++)
_v[i, k] = 0;
_v[k, k] = 1;
}
}
// Main iteration loop for the singular values.
int pp = p - 1;
int iter = 0;
double eps = (float)Math.Pow(2, -23); // 2^-52 for double
double tiny = (float)Math.Pow(2, -100); // 2^-100 for float is an estimation by HelmutG
// Original: 2^-966 for double
while (p > 0)
{
int k, kase;
// Here is where a test for too many iterations would go.
// This section of the program inspects for
// negligible elements in the s and e arrays. On
// completion the variables kase and k are set as follows.
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for (k = p - 2; k >= -1; k--)
{
if (k == -1)
break;
if (Math.Abs(e[k]) <= tiny + eps * (Math.Abs(_s[k]) + Math.Abs(_s[k + 1])))
{
e[k] = 0;
break;
}
}
if (k == p - 2)
{
kase = 4;
}
else
{
int ks;
for (ks = p - 1; ks >= k; ks--)
{
if (ks == k)
break;
float t = (ks != p ? Math.Abs(e[ks]) : 0) + (ks != k + 1 ? Math.Abs(e[ks - 1]) : 0);
if (Math.Abs(_s[ks]) <= tiny + eps * t)
{
_s[ks] = 0;
break;
}
}
if (ks == k)
{
kase = 3;
}
else if (ks == p - 1)
{
kase = 1;
}
else
{
kase = 2;
k = ks;
}
}
k++;
// Perform the task indicated by kase.
switch (kase)
{
// Deflate negligible s(p).
case 1:
{
float f = e[p - 2];
e[p - 2] = 0;
for (int j = p - 2; j >= k; j--)
{
float t = MathHelper.Hypotenuse(_s[j], f);
float cs = _s[j] / t;
float sn = f / t;
_s[j] = t;
if (j != k)
{
f = -sn * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
if (wantv)
{
for (int i = 0; i < _n; i++)
{
t = cs * _v[i, j] + sn * _v[i, p - 1];
_v[i, p - 1] = -sn * _v[i, j] + cs * _v[i, p - 1];
_v[i, j] = t;
}
}
}
}
break;
// Split at negligible s(k).
case 2:
{
float f = e[k - 1];
e[k - 1] = 0;
for (int j = k; j < p; j++)
{
float t = MathHelper.Hypotenuse(_s[j], f);
float cs = _s[j] / t;
float sn = f / t;
_s[j] = t;
f = -sn * e[j];
e[j] = cs * e[j];
if (wantu)
{
for (int i = 0; i < _m; i++)
{
t = cs * _u[i, j] + sn * _u[i, k - 1];
_u[i, k - 1] = -sn * _u[i, j] + cs * _u[i, k - 1];
_u[i, j] = t;
}
}
}
}
break;
// Perform one qr step.
case 3:
{
// Calculate the shift.
float scale = Math.Max(Math.Max(Math.Max(Math.Max(
Math.Abs(_s[p - 1]), Math.Abs(_s[p - 2])), Math.Abs(e[p - 2])),
Math.Abs(_s[k])), Math.Abs(e[k]));
float sp = _s[p - 1] / scale;
float spm1 = _s[p - 2] / scale;
float epm1 = e[p - 2] / scale;
float sk = _s[k] / scale;
float ek = e[k] / scale;
float b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2;
float c = (sp * epm1) * (sp * epm1);
float shift = 0;
if ((b != 0.0) | (c != 0.0))
{
shift = (float)Math.Sqrt(b * b + c);
if (b < 0.0)
shift = -shift;
shift = c / (b + shift);
}
float f = (sk + sp) * (sk - sp) + shift;
float g = sk * ek;
// Chase zeros.
for (int j = k; j < p - 1; j++)
{
float t = MathHelper.Hypotenuse(f, g);
float cs = f / t;
float sn = g / t;
if (j != k)
e[j - 1] = t;
f = cs * _s[j] + sn * e[j];
e[j] = cs * e[j] - sn * _s[j];
g = sn * _s[j + 1];
_s[j + 1] = cs * _s[j + 1];
if (wantv)
{
for (int i = 0; i < _n; i++)
{
t = cs * _v[i, j] + sn * _v[i, j + 1];
_v[i, j + 1] = -sn * _v[i, j] + cs * _v[i, j + 1];
_v[i, j] = t;
}
}
t = MathHelper.Hypotenuse(f, g);
cs = f / t;
sn = g / t;
_s[j] = t;
f = cs * e[j] + sn * _s[j + 1];
_s[j + 1] = -sn * e[j] + cs * _s[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (wantu && (j < _m - 1))
{
for (int i = 0; i < _m; i++)
{
t = cs * _u[i, j] + sn * _u[i, j + 1];
_u[i, j + 1] = -sn * _u[i, j] + cs * _u[i, j + 1];
_u[i, j] = t;
}
}
}
e[p - 2] = f;
iter = iter + 1;
}
break;
// Convergence.
case 4:
{
// Make the singular values positive.
if (_s[k] <= 0.0)
{
_s[k] = (_s[k] < 0.0 ? -_s[k] : 0);
if (wantv)
{
for (int i = 0; i <= pp; i++)
_v[i, k] = -_v[i, k];
}
}
// Order the singular values.
while (k < pp)
{
if (_s[k] >= _s[k + 1])
break;
float t = _s[k];
_s[k] = _s[k + 1];
_s[k + 1] = t;
if (wantv && (k < _n - 1))
{
for (int i = 0; i < _n; i++)
{
t = _v[i, k + 1];
_v[i, k + 1] = _v[i, k];
_v[i, k] = t;
}
}
if (wantu && (k < _m - 1))
{
for (int i = 0; i < _m; i++)
{
t = _u[i, k + 1];
_u[i, k + 1] = _u[i, k];
_u[i, k] = t;
}
}
k++;
}
iter = 0;
p--;
}
break;
}
}
}
public void SetWithArrayShouldThrowArgumentNullException()
{
VectorF v = new VectorF(1);
v.Set((float[])null);
}
//--------------------------------------------------------------
/// <summary>
/// Creates the eigenvalue decomposition of the given matrix.
/// </summary>
/// <param name="matrixA">The square matrix A.</param>
/// <exception cref="ArgumentNullException">
/// <paramref name="matrixA"/> is <see langword="null"/>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="matrixA"/> is non-square (rectangular).
/// </exception>
public EigenvalueDecompositionF(MatrixF matrixA)
{
if (matrixA == null)
throw new ArgumentNullException("matrixA");
if (matrixA.IsSquare == false)
throw new ArgumentException("The matrix A must be square.", "matrixA");
_n = matrixA.NumberOfColumns;
_d = new VectorF(_n);
_e = new VectorF(_n);
_isSymmetric = matrixA.IsSymmetric;
if (_isSymmetric)
{
_v = matrixA.Clone();
// Tridiagonalize.
ReduceToTridiagonal();
// Diagonalize.
TridiagonalToQL();
}
else
{
_v = new MatrixF(_n, _n);
// Abort if A contains NaN values.
// If we continue with NaN values, we run into an infinite loop.
for (int i = 0; i < _n; i++)
{
for (int j = 0; j < _n; j++)
{
if (Numeric.IsNaN(matrixA[i, j]))
{
_e.Set(float.NaN);
_v.Set(float.NaN);
_d.Set(float.NaN);
return;
}
}
}
// Storage of nonsymmetric Hessenberg form.
MatrixF matrixH = matrixA.Clone();
// Working storage for nonsymmetric algorithm.
float[] ort = new float[_n];
// Reduce to Hessenberg form.
ReduceToHessenberg(matrixH, ort);
// Reduce Hessenberg to real Schur form.
HessenbergToRealSchur(matrixH);
}
}
public void SetWithIListShouldThrowArgumentNullException()
{
VectorF v = new VectorF(1);
v.Set((IList<float>)null);
}
public SingularValueDecompositionF(MatrixF matrixA)
{
if (matrixA == null)
{
throw new ArgumentNullException("matrixA");
}
// Derived from LINPACK code.
// Initialize.
_m = matrixA.NumberOfRows;
_n = matrixA.NumberOfColumns;
MatrixF matrixAClone = matrixA.Clone();
if (_m < _n)
{
throw new ArgumentException("The number of rows must be greater than or equal to the number of columns.", "matrixA");
}
int nu = Math.Min(_m, _n);
_s = new VectorF(Math.Min(_m + 1, _n));
_u = new MatrixF(_m, nu); //Jama getU() returns new Matrix(U,_m,Math.min(_m+1,_n)) ?!
_v = new MatrixF(_n, _n);
float[] e = new float[_n];
float[] work = new float[_m];
// Abort if A contains NaN values.
// If we continue with NaN values, we run into an infinite loop.
for (int i = 0; i < _m; i++)
{
for (int j = 0; j < _n; j++)
{
if (Numeric.IsNaN(matrixA[i, j]))
{
_u.Set(float.NaN);
_v.Set(float.NaN);
_s.Set(float.NaN);
return;
}
}
}
// By default, we calculate U and V. To calculate only U or V we can set one of the following
// two constants to false. (This optimization is not yet tested.)
const bool wantu = true;
const bool wantv = true;
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
int nct = Math.Min(_m - 1, _n);
int nrt = Math.Max(0, Math.Min(_n - 2, _m));
for (int k = 0; k < Math.Max(nct, nrt); k++)
{
if (k < nct)
{
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[k].
// Compute 2-norm of k-th column without under/overflow.
_s[k] = 0;
for (int i = k; i < _m; i++)
{
_s[k] = MathHelper.Hypotenuse(_s[k], matrixAClone[i, k]);
}
if (_s[k] != 0)
{
if (matrixAClone[k, k] < 0)
{
_s[k] = -_s[k];
}
for (int i = k; i < _m; i++)
{
matrixAClone[i, k] /= _s[k];
}
matrixAClone[k, k] += 1;
}
_s[k] = -_s[k];
}
for (int j = k + 1; j < _n; j++)
{
if ((k < nct) && (_s[k] != 0))
{
// Apply the transformation.
float t = 0;
for (int i = k; i < _m; i++)
{
t += matrixAClone[i, k] * matrixAClone[i, j];
}
t = -t / matrixAClone[k, k];
for (int i = k; i < _m; i++)
{
matrixAClone[i, j] += t * matrixAClone[i, k];
}
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
e[j] = matrixAClone[k, j];
}
if (wantu & (k < nct))
{
// Place the transformation in U for subsequent back
// multiplication.
for (int i = k; i < _m; i++)
{
_u[i, k] = matrixAClone[i, k];
}
}
if (k < nrt)
{
// Compute the k-th row transformation and place the
// k-th super-diagonal in e[k].
// Compute 2-norm without under/overflow.
e[k] = 0;
for (int i = k + 1; i < _n; i++)
{
e[k] = MathHelper.Hypotenuse(e[k], e[i]);
}
if (e[k] != 0)
{
if (e[k + 1] < 0)
{
e[k] = -e[k];
}
for (int i = k + 1; i < _n; i++)
{
e[i] /= e[k];
}
e[k + 1] += 1;
}
e[k] = -e[k];
if ((k + 1 < _m) && (e[k] != 0))
{
// Apply the transformation.
for (int i = k + 1; i < _m; i++)
{
work[i] = 0;
}
for (int j = k + 1; j < _n; j++)
{
for (int i = k + 1; i < _m; i++)
{
work[i] += e[j] * matrixAClone[i, j];
}
}
for (int j = k + 1; j < _n; j++)
{
float t = -e[j] / e[k + 1];
for (int i = k + 1; i < _m; i++)
{
matrixAClone[i, j] += t * work[i];
}
}
}
if (wantv)
{
// Place the transformation in V for subsequent
// back multiplication.
for (int i = k + 1; i < _n; i++)
{
_v[i, k] = e[i];
}
}
}
}
// Set up the final bidiagonal matrix or order p.
int p = Math.Min(_n, _m + 1);
if (nct < _n)
{
_s[nct] = matrixAClone[nct, nct];
}
if (_m < p)
{
_s[p - 1] = 0;
}
if (nrt + 1 < p)
{
e[nrt] = matrixAClone[nrt, p - 1];
}
e[p - 1] = 0;
// If required, generate U.
if (wantu)
{
for (int j = nct; j < nu; j++)
{
for (int i = 0; i < _m; i++)
{
_u[i, j] = 0;
}
_u[j, j] = 1;
}
for (int k = nct - 1; k >= 0; k--)
{
if (_s[k] != 0)
{
for (int j = k + 1; j < nu; j++)
{
float t = 0;
for (int i = k; i < _m; i++)
{
t += _u[i, k] * _u[i, j];
}
t = -t / _u[k, k];
for (int i = k; i < _m; i++)
{
_u[i, j] += t * _u[i, k];
}
}
for (int i = k; i < _m; i++)
{
_u[i, k] = -_u[i, k];
}
_u[k, k] = 1 + _u[k, k];
for (int i = 0; i < k - 1; i++)
{
_u[i, k] = 0;
}
}
else
{
for (int i = 0; i < _m; i++)
{
_u[i, k] = 0;
}
_u[k, k] = 1;
}
}
}
// If required, generate V.
if (wantv)
{
for (int k = _n - 1; k >= 0; k--)
{
if ((k < nrt) & (e[k] != 0.0))
{
for (int j = k + 1; j < nu; j++)
{
float t = 0;
for (int i = k + 1; i < _n; i++)
{
t += _v[i, k] * _v[i, j];
}
t = -t / _v[k + 1, k];
for (int i = k + 1; i < _n; i++)
{
_v[i, j] += t * _v[i, k];
}
}
}
for (int i = 0; i < _n; i++)
{
_v[i, k] = 0;
}
_v[k, k] = 1;
}
}
// Main iteration loop for the singular values.
int pp = p - 1;
int iter = 0;
double eps = (float)Math.Pow(2, -23); // 2^-52 for double
double tiny = (float)Math.Pow(2, -100); // 2^-100 for float is an estimation by HelmutG
// Original: 2^-966 for double
while (p > 0)
{
int k, kase;
// Here is where a test for too many iterations would go.
// This section of the program inspects for
// negligible elements in the s and e arrays. On
// completion the variables kase and k are set as follows.
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for (k = p - 2; k >= -1; k--)
{
if (k == -1)
{
break;
}
if (Math.Abs(e[k]) <= tiny + eps * (Math.Abs(_s[k]) + Math.Abs(_s[k + 1])))
{
e[k] = 0;
break;
}
}
if (k == p - 2)
{
kase = 4;
}
else
{
int ks;
for (ks = p - 1; ks >= k; ks--)
{
if (ks == k)
{
break;
}
float t = (ks != p ? Math.Abs(e[ks]) : 0) + (ks != k + 1 ? Math.Abs(e[ks - 1]) : 0);
if (Math.Abs(_s[ks]) <= tiny + eps * t)
{
_s[ks] = 0;
break;
}
}
if (ks == k)
{
kase = 3;
}
else if (ks == p - 1)
{
kase = 1;
}
else
{
kase = 2;
k = ks;
}
}
k++;
// Perform the task indicated by kase.
switch (kase)
{
// Deflate negligible s(p).
case 1:
{
float f = e[p - 2];
e[p - 2] = 0;
for (int j = p - 2; j >= k; j--)
{
float t = MathHelper.Hypotenuse(_s[j], f);
float cs = _s[j] / t;
float sn = f / t;
_s[j] = t;
if (j != k)
{
f = -sn * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
if (wantv)
{
for (int i = 0; i < _n; i++)
{
t = cs * _v[i, j] + sn * _v[i, p - 1];
_v[i, p - 1] = -sn * _v[i, j] + cs * _v[i, p - 1];
_v[i, j] = t;
}
}
}
}
break;
// Split at negligible s(k).
case 2:
{
float f = e[k - 1];
e[k - 1] = 0;
for (int j = k; j < p; j++)
{
float t = MathHelper.Hypotenuse(_s[j], f);
float cs = _s[j] / t;
float sn = f / t;
_s[j] = t;
f = -sn * e[j];
e[j] = cs * e[j];
if (wantu)
{
for (int i = 0; i < _m; i++)
{
t = cs * _u[i, j] + sn * _u[i, k - 1];
_u[i, k - 1] = -sn * _u[i, j] + cs * _u[i, k - 1];
_u[i, j] = t;
}
}
}
}
break;
// Perform one qr step.
case 3:
{
// Calculate the shift.
float scale = Math.Max(Math.Max(Math.Max(Math.Max(
Math.Abs(_s[p - 1]), Math.Abs(_s[p - 2])), Math.Abs(e[p - 2])),
Math.Abs(_s[k])), Math.Abs(e[k]));
float sp = _s[p - 1] / scale;
float spm1 = _s[p - 2] / scale;
float epm1 = e[p - 2] / scale;
float sk = _s[k] / scale;
float ek = e[k] / scale;
float b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2;
float c = (sp * epm1) * (sp * epm1);
float shift = 0;
if ((b != 0.0) | (c != 0.0))
{
shift = (float)Math.Sqrt(b * b + c);
if (b < 0.0)
{
shift = -shift;
}
shift = c / (b + shift);
}
float f = (sk + sp) * (sk - sp) + shift;
float g = sk * ek;
// Chase zeros.
for (int j = k; j < p - 1; j++)
{
float t = MathHelper.Hypotenuse(f, g);
float cs = f / t;
float sn = g / t;
if (j != k)
{
e[j - 1] = t;
}
f = cs * _s[j] + sn * e[j];
e[j] = cs * e[j] - sn * _s[j];
g = sn * _s[j + 1];
_s[j + 1] = cs * _s[j + 1];
if (wantv)
{
for (int i = 0; i < _n; i++)
{
t = cs * _v[i, j] + sn * _v[i, j + 1];
_v[i, j + 1] = -sn * _v[i, j] + cs * _v[i, j + 1];
_v[i, j] = t;
}
}
t = MathHelper.Hypotenuse(f, g);
cs = f / t;
sn = g / t;
_s[j] = t;
f = cs * e[j] + sn * _s[j + 1];
_s[j + 1] = -sn * e[j] + cs * _s[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (wantu && (j < _m - 1))
{
for (int i = 0; i < _m; i++)
{
t = cs * _u[i, j] + sn * _u[i, j + 1];
_u[i, j + 1] = -sn * _u[i, j] + cs * _u[i, j + 1];
_u[i, j] = t;
}
}
}
e[p - 2] = f;
iter = iter + 1;
}
break;
// Convergence.
case 4:
{
// Make the singular values positive.
if (_s[k] <= 0.0)
{
_s[k] = (_s[k] < 0.0 ? -_s[k] : 0);
if (wantv)
{
for (int i = 0; i <= pp; i++)
{
_v[i, k] = -_v[i, k];
}
}
}
// Order the singular values.
while (k < pp)
{
if (_s[k] >= _s[k + 1])
{
break;
}
float t = _s[k];
_s[k] = _s[k + 1];
_s[k + 1] = t;
if (wantv && (k < _n - 1))
{
for (int i = 0; i < _n; i++)
{
t = _v[i, k + 1];
_v[i, k + 1] = _v[i, k];
_v[i, k] = t;
}
}
if (wantu && (k < _m - 1))
{
for (int i = 0; i < _m; i++)
{
t = _u[i, k + 1];
_u[i, k + 1] = _u[i, k];
_u[i, k] = t;
}
}
k++;
}
iter = 0;
p--;
}
break;
}
}
}
